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ps10s08sol

# ps10s08sol - = MC = 60 ⇒ Q = 120 Total proﬁt...

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1. Question 1 (a) P = 1. Q = 500 - 10 P = 500 - 10 × 1 = 490. CS = (50 - 1) × 490 2 . profit = 490 × 1 - 500 - 490 = - 500 (b) Revenue = TC PQ = 500 + Q . Q = 500 - 10 P . P (500 - 10 P ) = 500+500 - 10 P P = 25 . 5 - 550 . 25 2 . 04. Q 500 - 10 × 2 . 04 = 479 . 6. CS (50 - 2 . 04)479 . 6 2 = 11500 . 81. Profit = 0. Yes, there is deadweight loss. 2. Question 2 (a) Q T = 150 - 3 2 P + 50 - 1 2 P = 200 - 2 P P = 100 - 1 2 Q T MR = 100 - Q T = MC = 5 Q T = 95. P = 52 . 5. Profit = 52 . 5 × 95 - 5 × 95 = 4512 . 5. Q trojan = 150 - 3 2 (52 . 5) = 71 . 25. Q westwood = 50 - 1 2 (52 . 5) = 23 . 75. CS trojan = 1 2 (100 - 52 . 5)71 . 25 = 1692 . 19. CS westwood = 1 2 (100 - 52 . 5)23 . 75 = 564 . 06. (b) (c) MR trojan = 100 - 4 3 Q trojan = 5 Q trojan = 71 . 25. MR westwood = 100 - 4 Q westwood = 5 Q westwood = 23 . 75. P = 52 . 5 , profit = 4512 . 5 CS trojan = 1692 . 19 CS westwood = 564 . 06. (d) MC = 100. 3. Question 3 (a) 300 - Q 2 - 2 Q 1 = 60 = 300 - Q 1 - 2 Q 2 . Since both firms are identical. Thus, Q 1 = Q 2 = Q . Thus, 240 = 3 Q Q = 80. Profit of each firm is (300 - 80 - 80)80 - 60 ×
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Unformatted text preview: = MC = 60 ⇒ Q = 120. Total proﬁt is (300-120)-60 × 120 = 14400. This evenly divided between ﬁrms. (c) Its quantity and proﬁt will be equal to the combined quantity and proﬁt of part b. (d) Suppose the original agreement is to evenly share. Then 300-60-2 Q 2 = 60 ⇒ Q 2 = 90. Proﬁt of ﬁrm 1 is (300-90-60)60-60 × 60 = 5400. Proﬁt of ﬁrm 2 is (300-90-60)90-60 × 90 = 8100. (e) 300-Q 2-2 Q 1 = 60 and 30 = 300-Q 1-2 Q 2 . Thus Q 1 = 70 , Q 2 = 100. (f) Firm 2 will produce, and 30 = 300-2 Q ⇒ Q = 135. Firm 1 produce nothing. Price is P = 165. Firm 1 has incentive to cheat. 1...
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